Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#509 | C2 | semidirect |
| 2. C11×#493 | C2 | semidirect |
| 3. C11×#443 | C2 | semidirect |
| 4. C11×#364 | C2 | semidirect |
| 5. C11×#361 | C2 | semidirect |
| 20. C11×Q16 | D4 | semidirect |
| 26. C11×D8 | D4 | semidirect |
| 34. #2213 | C11 | direct (N × H) |
| 50. #509 | C2×C11 | semidirect |
| 51. #493 | C2×C11 | semidirect |
| 52. #443 | C2×C11 | semidirect |
| 53. #364 | C2×C11 | semidirect |
| 54. #361 | C2×C11 | semidirect |
| 81. Q16 | D4×C11 | semidirect |
| 87. D8 | D4×C11 | semidirect |
| 95. C11 | #2213 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#509 | 2 |
| C11×#493 | 2 |
| C11×#443 | 2 |
| C11×#364 | 2 |
| C11×#361 | 2 |
| #2213 | 11 |